The weightiest argument against capital punishment is the commandment, "Thou shalt not kill." Many people would refuse to kill, no matter how many people told them it was okay. And they don't want the State to kill on their behalf. I believe this is an honorable position; to be ethically sound, however, it should be consistently held across all societal questions.
For instance . . .
Abortion. If we're going to spare murderers, who obviously deserve to be punished, then we must spare the unborn, who obviously don't deserve to be punished. Any opponent of capital punishment who is not also categorically opposed to abortion loses my respect instantly.
War. If there is no process of law that can justify killing a convicted murderer, then I see no legal reason to kill someone in the service of another country (especially one who is not actively seeking to kill someone else). That means attacking members of an opposing State's military (or members of a terrorist gang operating internationally), just because they are in the service of the enemy -- riding a boat, sitting down to dinner, on a train, attending a planning conference, tinkering with a bomb that hasn't been deployed yet, standing guard -- is obviously wrong. Even maintaining armed forces that have the means to kill endorses the possible use of those means. No "State of War" can condone killing, if killing is always wrong; likewise, possessing arms and training people to kill cannot be condoned, if killing is always wrong. But if killing is not always wrong, then "thou shalt not kill" doesn't automatically apply to capital punishment.
An armed police. Police are trained not to wave their weapons around, not to solve problems with weapons that could be solved without them; nevertheless, they are armed, and they are trained to use those arms. But if killing is wrong simpliciter, and killing on our behalf is as repugnant as doing the killing ourselves, then police should not be equipped with the means to kill.
Now, many opponents of capital punishment will immediately reply with a host of objections. Chief among them is probably the argument from self-defense. I agree with that argument (though many committed pacifists would not), but that means that the opponent of capital punishment has forfeited the moral high ground and is willing to argue cases. For that matter, any exceptions to the categorical refusal to kill (directly, or indirectly through the State) means that killing is sometimes, somehow justified. All this means that the opponent of capital punishment has to answer the case for capital punishment; in doing so, employing the usual sanctimony is merely a sign of the weakness of one's argument, rather like the old preacher who had a hand-written note in the margin of his sermon manuscript that read, "Argument poor, yell like blazes."
Deprived of the moral high ground, most opponents of capital punishment fall back on utilitarian arguments. But deciding questions of justice on utilitarian grounds is inherently dangerous, and will lead to a society that values life much less than even our current society does.